1. Field of the Invention
The present invention relates generally to pulse-reshaping optical fibers and transmission systems utilizing such fibers, and particularly to a pulse-compressing optical fiber.
2. Technical Background
There exists a need for a cost-effective way to increase the information-carrying capacity of optical transmission systems. The term "optical transmission system" refers to any system that uses optical signals to convey information across an optical waveguiding medium such as a single-mode optical fiber. Such optical systems include, but are not limited to, telecommunications systems, cable television systems, and local area networks (LANs). Wavelength-division-multiplexing (WDM) has been employed to increase the capacity of optical transmission systems. A WDM system employs a plurality of optical signal channels, with each channel being assigned a particular channel wavelength. In a WDM system, signal channels are generated, multiplexed, and transmitted over the optical transmission fiber. At the receiving end, the optical signal is demultiplexed such that each channel wavelength can be individually routed to a designated receiver.
Time-division-multiplexing (TDM) has also been employed to increase the capacity of optical transmission systems by decreasing the width of the temporal window used to represent a binary bit of data. The upper capacity limit of TDM occurs when the transmitter electronics is incapable of generating pulses narrow enough to satisfy a predetermined pulse rate. For example, the given system might not be able to transmit pulses at a single wavelength channel data rate of more than 40 Gb/s. In order overcome this limitation and increase the data rate for a return-to-zero (RZ) modulation format, the output pulse train from the light source can be sent through a pulse compressor before being injected into the optical transmission line. The pulse compressor narrows the pulse width, permitting more pulses to be transmitted within a given time period. Conversely, on the receiver end of the transmission line, a pulse-shaping device expands the pulses to their original shape.
During transmission, pulses can disperse or widen as the signal travels along the fiber, resulting in pulses which eventually overlap if they are not initially spaced apart sufficiently. This dispersion similarly limits the data rate capacity of the fiber, and the ability to utilize time-division-multiplexing. Different approaches have been used to overcome dispersion, including dispersion-decreasing fibers and soliton pulses which maintain their characteristic shape when transmitted over long distances. Pulse compression can occur intrinsically in an axially-nonuniform optical fiber (a fiber whose dispersion decreases monotonically from one end to the other), with dispersion decreasing approximately exponentially with distance to attain soliton propagation.
This type of pulse-reshaping relies on a slight imbalance between the competing self-phase modulation (SPM) and dispersion effects in the fiber. For pulse compression, the fiber is designed to have a small residual amount of uncompensated SPM, causing a pulse frequency chirp that decreases the energy in the tails of the pulse via dispersion. For pulse expansion, the fiber is designed to have a small residual amount of uncompensated dispersion, causing a frequency chirp of the opposite sign that increases the energy in the tails of the pulse via SPM. Propagation in the opposite direction changes a pulse-compressing fiber to a pulse-expanding fiber. It has been shown numerically that if the reshaping is allowed to occur adiabatically (slowly) on the scale of the "dispersive length," then all the energy of the original pulse is transferred to the reshaped pulse and no dispersive waves are generated. The adiabatic condition means that the product of the rate of change of the pulse width times the dispersive length must be much less than unity. In practice, the fiber length L should be such that EQU 2 L.sub.D &lt;L&lt;10 L.sub.D (1)
where L.sub.D is the "dispersive length." The dispersive length is given by EQU L.sub.D =T.sub.o.sup.2 /.vertline..beta..sub.2.vertline. (2)
where T.sub.o is the 1/e characteristic pulse width of the optical field, and the group velocity dispersion .beta..sub.2 in ps.sup.2 /nm is given by the equation EQU .beta..sub.2 =-.lambda..sup.2 D/2.pi.c (3)
where .lambda. is the wavelength, D is dispersion in units of ps/nm-km, and c is the speed of light. For a hyperbolically-shaped soliton, the full-width half-maximum T.sub.fwhm of the pulse equals 1.763 (T.sub.o). Thus, EQU L.sub.D =[T.sup.2.sub.fwhm.multidot.2.pi.c]/[(1.763).sup.2.multidot.D.lambda..sup. 2 ] (4)
Taking the optical transmission window centered at 1550 nm wavelength as an example, the dispersive length L.sub.D would be approximately (T.sup.2.sub.fwhm /4D) at the wavelength of 1550 nm. If the dispersion D at the input end of a pulse compression fiber (z=0) is 10 ps/nm-km, and the full-width half-maximum value T.sub.fwhm is 8 ps, then the dispersive length L.sub.D would be 1.6 km. The length L of the compression fiber would then be determined by relationship (1). The minimum and maximum lengths given by relationship (1) in this example would be 3.2 km and 16 km, respectively. Length L should not be made longer than the length necessary to achieve the desired pulse compression, because longer lengths would unnecessarily increase system loss. A particularly suitable fiber length is that which adiabatically compresses the pulse and is approximately 5 L.sub.D. For the above example, this length is about 8 km.
Fiber length L would therefore normally be much greater than 2L.sub.D for optimum performance. However, shorter lengths (L down to 2L.sub.D) could be used if the output pulse train was spectrally enhanced device before the pulse train is injected into the input end of the pulse compression fiber. Such spectral enhancement can be accomplished using a sufficiently long length (about 1-2 km) of dispersion-shifted (DS) single-mode optical fiber to cause self phase modulation.
Prior pulse-compression/expansion schemes in axially-varying fiber have used two approaches: 1) fiber whose diameter continuously changes along its length to impart the desired dispersion-decreasing profile; or 2) fiber composed of many alternating segments of fibers having high and low anomalous dispersion which, in effect, spatially separate the SPM and dispersion-reshaping components. In either case, the fiber has employed either a step-index profile (as in standard nondispersion-shifted fiber) or one of various dispersion-shifted transmission fiber profiles. All commercially-available fibers suffer from the same rather large dispersion slope of at least 0.04 ps/nm.sup.2 -km, which limits the wavelength range over which useful pulse compression can be achieved in an optical transmission system.
The pulse-reshaping fiber should be operative over a large range of wavelengths. For example, it is highly desirable to have a reshaping fiber that operates over the entire erbium (Er) amplification band. In that case, a single fiber could take the broad wavelength output from a wavelength-division-multiplexed array of electro-absorption modulators and simultaneously compress all wavelength channels to the same required pulse width. Such an integrated and compact device would be very useful for high data rate transmission.
The pulse-reshaping fiber should also be operative over a large range of pulse widths and compression factors. The compression factor is defined as the ratio of input to output pulse widths. If the adiabatic condition is met, the effective area of the fiber is approximately constant, and the dispersion exponentially decreases along the fiber with a decay rate equal to the sum of the loss rate .alpha. of the fiber per kilometer and the rate .rho. at which the pulse width decreases over distance. This means that the rate of dispersion change must be greater than the loss rate in order to compress the pulse as it propagates. However, dispersion is also a function of wavelength. The linear component of this dependence is known as dispersion slope. High dispersion slope implies a large dispersion change. Therefore, fibers with high dispersion slope exhibit a compression factor having a large wavelength dependence. One representative example of such a DS fiber profile is disclosed in U.S. Pat. No. 5,504,829, having a dispersion slope of 0.08 ps/nm-km (given an initial pulse width of 8 ps, fiber loss of 0.2 dB/km, fiber length of 10 km, and input pulse power equal to the fundamental soliton power). If this fiber were designed for four times (4.times.) compression by exponentially varying the dispersion from 10 to 1.55 ps/nm-km at 1550 nm, then due to the dispersion slope at 1570 nm the dispersion would vary from 11.6 to 3.15 ps/nm-km, and the compression factor would be 2.3. Moreover, at 1530 nm the dispersion would vary from positive 8.4 to negative 0.05 ps/nm-km, and the compression factor would become virtually impossible to approximate. Numerical simulations are required to fully illustrate the associated problems of dispersion slope. Solving the nonlinear Schodinger equation, the output pulse width at 1550 nm wavelength is 2.0 ps, whereas it is 1.6 ps at 1530 nm, and 3.11 ps at 1570 nm. This corresponds to compression factors of 4.times., 5.times., and 2.6.times. for 1550 nm, 1530 nm, and 1570 nm, respectively. Not only are the compression factors different, but pulse distortion occurs at smaller wavelengths where the output pulse width is shorter. This can be shown graphically, for example with reference to FIG. 1 herein, where the output pulses at 1550 nm, 1570 nm, and 1530 nm are represented by curves 12, 14, and 16, respectively, plotted against the input pulse 10 for comparison. The temporal output intensity of a conventional soliton pulse is plotted for the three wavelengths in logarithmic scale for FIG. 1(a) and linear scale for FIG. 1(B), with the numerals depicting curves in FIG. 1(b) being primed. The logarithmic scale reflects the differences in the low-intensity tails of the pulse at the three wavelengths, whereas the linear scale demonstrates the differences in the peak intensity and widths of the pulses at each of the three wavelengths.
These differences are a direct consequence of finite dispersion slope, especially near the output end of the fiber. Pulse distortion in a transmitter leads to dispersive wave generation, and an undesirable continuous-wave background. The above example demonstrates that high dispersion slope is detrimental to optical signal transmission where broad wavelength band compression and narrow pulse output are desired.
The broadband problem introduced by high dispersion slope fiber can be overcome by utilizing different high-slope pulse-compression fibers for each input channel of the WDM system, but tuning each fiber to have the same initial dispersion and rate of change. However, this solution is commercially unacceptable, as it greatly increases the amount of pulse compression fiber required for the system, and overly complicates the design and manufacture of the system.
Even if an optical transmission system utilized only one wavelength channel, it would still be advantageous to employ a pulse-compression fiber having low slope, since finite slope acts to distort the pulse shape (especially for short pulses near the zero-dispersion wavelength in the fiber).
To quantify the requirement on dispersion slope needed to maintain the desired pulse-reshaping performance over a broad wavelength range, consider the wavelength variation on the ratio of input to output dispersion at other wavelengths: EQU D(.lambda..sub.C,L)/D(.lambda..sub.C,0).times.[D(.lambda..sub. C,0)+(.lambda..sub.C -.lambda..sub.E)S(.lambda..sub.C,0)]/[D(.lambda..sub.C,L)+(.lambda..sub.C -.lambda..sub.E)S(.lambda..sub.C,L)]&gt;(1-.eta.) (5)
where .lambda..sub.C is the center wavelength of the operating window, .lambda..sub.E is the wavelength at the edge of the operating window, D(.lambda.,z) is the dispersion at wavelength .lambda. and length z, S(.lambda.,z) is the dispersion slope at wavelength .lambda. and length z, .eta. is the factor by which the dispersion ratio can differ from the optimal value D(.lambda..sub.C,0)/D(.lambda..sub.C,L). The factor .eta. also represents the factor by which the output pulse widths differ across the wavelength band. Equation (5) can be rewritten in terms of the difference between the initial and final dispersion slopes: EQU [(1-.eta.)S(.lambda..sub.C,L)D(.lambda..sub.C,0)/D(.lambda..sub. C,L)]-S(.lambda..sub.C,0)&lt;D(.lambda..sub.C 0).eta./(.lambda..sub.C -.lambda..sub.E) (6)
Assuming that the system can tolerate at 10% difference in dispersion, then 1-.eta. equals 0.9. Further assume as in the previous example that (.lambda..sub.C -.lambda..sub.E) equals 20 nm, D(.lambda..sub.C,0) equals 10, and D(.lambda..sub.C,L) equals 1.55. Then equation (6) reduces to: EQU .vertline.5.8 S(.lambda..sub.C,L)-S(.lambda..sub.C,0).vertline.&lt;0.05 (6')
If there is no slope change, then S(.lambda..sub.C,0)=S(.lambda..sub.C,L)&lt;0.01. If S(.lambda..sub.C,0)=0.03 then S(.lambda..sub.C,L)&lt;0.014, and if S(.lambda..sub.C,0)=0.07 then S(.lambda..sub.C,L)&lt;0.02. Also, a larger target dispersion ratio lowers the upper limit on the final dispersion slope. For most cases of practical interest, this broadband criterion sets a final slope limit somewhere between 0.01 and 0.02 ps/nm.sup.2 /km.
A second slope-limiting criterion arises from distortion of short pulses caused by third-order dispersion. A third-order dispersive length (analogous to the second order dispersive length previously defined) is useful: EQU L.sub.D =T.sub.o.sup.3 /.vertline..beta..sub.3.vertline. (7)
where .beta..sub.3 =-.lambda..sup.4 S/(2.pi.c).sup.2. Because the pulse width and dispersion slope are functions of distance, the equation in dispersion-decreasing fiber becomes: EQU L.sub.D =&lt;T.sub.o &gt;.sup.3 /.vertline.&lt;.beta..sub.3 &gt;.vertline. (8)
where &lt;T.sub.o &gt;=T.sub.o (0)(1-e.sup.-.rho.L)/.rho.L, &lt;.beta..sub.3 &gt;=(0)(1-e.sup.-bL)/bL, and .rho. and b are the exponential decay rates of the pulse width and dispersion slope, respectively. For the third order effects to be negligible, the fiber length L must be much less than the third order dispersive length (L&lt;&lt;L'.sub.D). A factor of ten is sufficient (10 L&lt;L'.sub.D). For an 8 ps initial pulse width, a 10 km fiber, and dispersion changing from 10 to 1.55, the average slope should thus be less than 0.09 ps/nm.sup.2 /km (which is not a significant restriction). However, the cubed pulse width dependence greatly restricts shorter pulse compression. For example, the average slope of a 5 ps pulse should be less than 0.022. In addition, if the dispersion drop is from 10 to 1, then the 5 ps slope becomes 0.013. Values of dispersion slope at the low dispersion end of the fiber should be lower than 0.025 ps/nm.sup.2 -km to meet the slope criterion for most practical optical signal transmission applications.